Objects with "solid" surfaces
Yes, but probably not the way you are thinking. You might try a “Floor” constraint, or some of the other constraints for that matter. Another option might be the snapping setting for transform tools. Setting it to Vertex -&gt; closest may or may not yield desirable operation.
Physics, on the other hand, can definitely work with non uniform surfaces, but do not operate unless time is moving forward: they will likely be unhelpful while posing a stationary scene as you can transform two rigid bodies to intersect eachother if animation is not playing. Once it starts playing, of course, they will jump apart. But with blender time stopped, blender physics is stopped too.